On the Economization of Stabilized Runge‐Kutta Methods with Applications to Parabolic Initial Value Problems

Abstract

AbstractA modification of Runge ‐ Kutta methods is analysed which leads for important classes of parabolic differential equations to a considerable reduction of the computational effort. The main characteristic of the modified methods is the replacement of the right hand side function of the differential equation by a “cheaper” function with roughly the same Jacobian matrix. Numerical experiments are reported and the results are compared with the results obtained by the unmodified Runge‐Kutta method and by an ADI method.